Electrically conductive contact elements (e.g., probes) can make electrical connections between electrical devices. For example, such contact elements can be disposed between electrical devices to make electrical connections between the devices. As another example, such contact elements can be part of one electronic device, and the contact elements can be moved into contact with terminals of another electronic device to form pressure-based electrical connections with the other device. Testing of newly manufactured electronic devices (e.g., semiconductor dies) is one example of an application for the foregoing. Regardless of the application, however, vertical contact elements can be advantageous as can contact elements that exhibit a non-linear spring response to forces through the contact element.